Page No 168:

Question 1:

Define the principal focus of a concave mirror.

Answer:

Light
rays that are parallel to the principal
axis of a concave mirror converge at a specific point on its
principal axis after reflecting from the mirror. This point is known
as the principal focus of the concave mirror.

Page No 168:

Question 2:

The radius of curvature of a spherical mirror is 20 cm. What is its
focal length?

Answer:

Radius
of curvature, R
= 20 cm

Radius
of curvature of a spherical mirror = 2 × Focal length (f)

R
= 2f

Hence,
the focal length of the given spherical
mirror is 10 cm.

Page No 168:

Question 3:

Name the mirror that can give an erect and enlarged image of an
object.

Answer:

When
an object is placed between the pole and
the principal focus of a concave mirror,
the image formed is virtual, erect, and enlarged.

Page No 168:

Question 4:

Why do we prefer a convex mirror as a rear-view mirror in vehicles?

Answer:

Convex
mirrors give a virtual, erect, and diminished image of the objects
placed in front of them. They are preferred as a rear-view mirror in
vehicles because they give a wider field of view, which allows the
driver to see most of the traffic behind him.

Page No 171:

Question 1:

Find the focal length of a convex mirror whose radius of curvature is
32 cm.

Answer:

Radius
of curvature, R
= 32 cm

Radius
of curvature = 2 × Focal length (f)

R
= 2f

Hence,
the focal length of the given convex mirror
is 16 cm.

Page No 171:

Question 2:

A
concave mirror produces three times
magnified (enlarged) real image of object placed at 10 cm in front of
it. Where is the image located?

Answer:

Magnification
produced by a spherical mirror is given by
the relation,

Let
the height of the object, ho
= h

Then,
height of the image, hI
= −3h
(Image formed is real)

Object
distance, u
= −10 cm

v
= 3 × (−10) = −30 cm

Here,
the negative sign indicates that an inverted image is formed at a
distance of 30 cm in front of the given concave mirror.

Page No 176:

Question 1:

A
ray of light travelling in air enters obliquely into water. Does the
light ray bend towards the normal or away from the normal? Why?

Answer:

The light ray bends towards
the normal.

When
a ray of light travels from an optically rarer medium to an optically
denser medium, it gets bent towards the
normal. Since water is optically denser than air, a ray of light
travelling from air into the water will bend towards the normal.

Page No 176:

Question 2:

Light
enters from air to glass having refractive index 1.50. What is the
speed of light in the glass? The speed of light in vacuum is 3 ×
108 m
s−1.

Answer:

Refractive
index of a medium nm
is given by,

Speed
of light in vacuum, c
= 3 × 108 m
s−1

Refractive
index of glass, ng
= 1.50

Speed
of light in the glass,

Page No 176:

Question 3:

Find out, from Table, the medium having highest optical density.
Also find the medium with lowest optical density.

Material

medium

Refractive index

Material medium

Refractive

index

Air

1.0003

Canada Balsam

1.53

Ice

1.31

-

-

Water

1.33

Rock salt

1.54

Alcohol

1.36

-

-

Kerosene

1.44

Carbon disulphide

1.63

Fused

quartz

1.46

Dense

flint glass

1.65

Turpentine oil

1.47

Ruby

1.71

Benzene

1.50

Sapphire

1.77

Crown

glass

1.52

Diamond

2.42

Answer:

Highest optical density = Diamond

Lowest optical density = Air

Optical density of a medium is directly related with the
refractive index of that medium. A medium which has the highest
refractive index will have the highest optical density and
vice-versa.

It can be observed from table 10.3 that diamond and air
respectively have the highest and lowest refractive index. Therefore,
diamond has the highest optical density and air has the lowest
optical density.

Page No 176:

Question 4:

You
are given kerosene, turpentine and water.
In which of these does the light travel fastest? Use the information
given in Table.

Material

medium

Refractive index

Material medium

Refractive

index

Air

1.0003

Canada Balsam

1.53

Ice

1.31

-

-

Water

1.33

Rock salt

1.54

Alcohol

1.36

-

-

Kerosene

1.44

Carbon disulphide

1.63

Fused

quartz

1.46

Dense

flint glass

1.65

Turpentine oil

1.47

Ruby

1.71

Benzene

1.50

Sapphire

1.77

Crown

glass

1.52

Diamond

2.42

Answer:

Speed
of light in a medium is given by the relation for refractive
index (nm).
The relation is given as

It
can be inferred from the relation that
light will travel the slowest in the material which has the highest
refractive index and travel the fastest in the material which has the
lowest refractive index.

It
can be observed from table 10.3 that the refractive
indices of kerosene, turpentine, and water are 1.44, 1.47, and 1.33
respectively. Therefore, light travels the fastest in water.

Page No 176:

Question 5:

The refractive index of diamond is 2.42. What is the meaning of this
statement?

Answer:

Refractive
index of a medium nm
is related to the speed of light in that medium v
by the relation:

Where, c
is the speed of light in vacuum/air

The
refractive index of diamond is 2.42. This suggests that the speed of
light in diamond will reduce by a factor 2.42 compared to its speed
in air.

Page No 184:

Question 1:

Define 1 dioptre of power of a lens.

Answer:

Power
of lens is defined as the reciprocal of its
focal length. If P
is the power of a lens of focal length F
in metres, then

The
S.I. unit of power of a lens is Dioptre. It is denoted by D.

1
dioptre is defined as the power of a lens
of focal length 1 metre.

∴1
D = 1 m−1

Page No 184:

Question 2:

A
convex lens forms a real and inverted image
of a needle at a distance of 50 cm from it. Where is the needle
placed in front of the convex lens if the image is equal to the size
of the object? Also, find the power of the lens.

Answer:

When
an object is placed at the centre of curvature,
2F1,
of a convex lens, its image is formed at the centre of curvature,
2F2,
on the other side of the lens. The image formed is inverted and of
the same size as the object, as shown in the given figure.

It
is given that the image of the needle is
formed at a distance of 50 cm from the convex lens. Hence, the needle
is placed in front of the lens at a distance of

50 cm.

Object
distance, u
= −50 cm

Image
distance, v
= 50 cm

Focal
length =f

According
to the lens formula,

Hence,
the power of the given lens is +4 D.

Page No 184:

Question 3:

Find the power of a concave lens of focal length 2 m.

Answer:

Focal length of concave lens, f = 2 m

Here, negative sign arises due to the divergent nature of concave lens.

Hence, the power of the given concave lens is −0.5 D.

Page No 185:

Question 1:

Which one of the following materials cannot be used to make a lens?

(a) Water

(b) Glass

(c) Plastic

(d) Clay

Answer:

(d) A lens allows light
to pass through it. Since clay does not show such property, it cannot
be used to make a lens.

Page No 185:

Question 2:

The image
formed by a concave mirror is observed to be virtual, erect and
larger than the object. Where should be the position of the object?

(a) Between
the principal focus and the centre of curvature

(b) At the
centre of curvature

(c) Beyond
the centre of curvature

(d) Between
the pole of the mirror and its principal focus.

Answer:

(d) When an object is
placed between the pole and principal focus of a concave mirror, the
image formed is virtual, erect, and larger than the object.

Page No 185:

Question 3:

Where
should an object be placed in front of a convex lens to get a real
image of the size of the object?

(a) At
the principal focus of the lens

(b) At
twice the focal length

(c) At
infinity

(d) Between
the optical centre of the lens and its principal focus.

Answer:

(b) When an object is
placed at the centre of curvature in front of a convex lens, its
image is formed at the centre of curvature on the other side of the
lens. The image formed is real, inverted, and of the same size as the
object.

Page No 185:

Question 4:

A
spherical mirror and a thin spherical lens have each a focal length
of −15 cm. The mirror and the lens
are likely to be

(a) both
concave

(b) both
convex

(c) the
mirror is concave and the lens is convex

(d) the
mirror is convex, but the lens is concave

Answer:

(a) By convention, the
focal length of a concave mirror and a concave lens are taken as
negative. Hence, both the spherical mirror and the thin spherical
lens are concave in nature.

Page No 186:

Question 5:

No matter
how far you stand from a mirror, your image appears erect. The mirror
is likely to be

(a) plane

(b) concave

(c) convex

(d) either
plane or convex

Answer:

(d) A convex mirror
always gives a virtual and erect image of smaller size of the object
placed in front of it. Similarly, a plane mirror will always give a
virtual and erect image of same size as that of the object placed in
front of it. Therefore, the given mirror could be either plane or
convex.

Page No 186:

Question 6:

Which of
the following lenses would you prefer to use while reading small
letters found in a dictionary?

(a) A
convex lens of focal length 50 cm

(b) A
concave lens of focal length 50 cm

(c) A
convex lens of focal length 5 cm

(d) A
concave lens of focal length 5 cm

Answer:

(c) A convex lens gives
a magnified image of an object when it is placed between the radius
of curvature and focal length. Also, magnification is more for convex
lenses having shorter focal length. Therefore, for reading small
letters, a convex lens of focal length 5 cm should be used.

Page No 186:

Question 7:

We
wish to obtain an erect image of an object,
using a concave mirror of focal length 15 cm. What should be the
range of distance of the object from the mirror? What is the nature
of the image? Is the image larger or smaller than the object? Draw a
ray diagram to show the image formation in this case.

Answer:

Range of object distance = 0
cm to15 cm

A
concave mirror gives an erect image when an object is placed between
its pole (P) and the principal focus (F).

Hence,
to obtain an erect image of an object from
a concave mirror of focal length 15 cm, the object must be placed
anywhere between the pole and the focus. The image formed will be
virtual, erect, and magnified in nature, as shown in the given
figure.

Page No 186:

Question 8:

Name the type of mirror used in the following situations.

(a) Headlights
of a car

(b) Side/rear-view
mirror of a vehicle

(c) Solar
furnace

Support
your answer with reason.

Answer:

(a) Concave (b)
Convex (c) Concave

Explanation

(a) Concave mirror is
used in the headlights of a car. This is because concave mirrors can
produce powerful parallel beam of light when the light source is
placed at their principal focus.

(b) Convex mirror is
used in side/rear view mirror of a vehicle. Convex mirrors give a
virtual, erect, and diminished image of the objects placed in front
of it. Because of this, they have a wide field of view. It enables
the driver to see most of the traffic behind him/her.

(c) Concave mirrors are
convergent mirrors. That is why they are used to construct solar
furnaces. Concave mirrors converge the light incident on them at a
single point known as principal focus. Hence, they can be used to
produce a large amount of heat at that point.

Page No 186:

Question 9:

One-half
of a convex lens is covered with a black paper. Will this lens
produce a complete image of the object? Verify your answer
experimentally. Explain your observations.

Answer:

The
convex lens will form complete image of an object, even if its one
half is covered with black paper. It can be understood by the
following two cases.

Case I

When the
upper half of the lens is covered

In
this case, a ray of light coming from the object will be refracted by
the lower half of the lens. These rays meet at the other side of the
lens to form the image of the given object, as shown in the following
figure.

Case
II

When the
lower half of the lens is covered

In
this case, a ray of light coming from the object is refracted by the
upper half of the lens. These rays meet at the other side of the lens
to form the image of the given object, as shown in the following
figure.

Page No 186:

Question 10:

An object
5 cm in length is held 25 cm away from a converging lens of focal
length 10 cm. Draw the ray diagram and find the position, size and
the nature of the image formed.

Answer:

Object
distance, u
= −25 cm

Object
height, ho
= 5 cm

Focal
length, f
= +10 cm

According
to the lens formula,

The
positive value of v
shows that the image is formed at the other side of the lens.

The
negative sign shows that the image is real and formed behind the
lens.

The
negative value of image height indicates that the image formed is
inverted.

The
position, size, and nature of image are shown in the following ray
diagram.

Page No 186:

Question 11:

A
concave lens of focal length 15 cm forms an
image 10 cm from the lens. How far is the object placed from the
lens? Draw the ray diagram.

Answer:

Focal
length of concave lens (OF1),
f = −15
cm

Image
distance, v
= −10 cm

According
to the lens formula,

The
negative value of u
indicates that the object is placed 30 cm in front of the lens. This
is shown in the following ray diagram.

Page No 186:

Question 12:

An
object is placed at a distance of 10 cm from a
convex mirror of focal length 15 cm. Find the position and nature of
the image.

Answer:

Focal
length of convex mirror, f
= +15 cm

Object
distance, u
= −10 cm

According
to the mirror formula,

The
positive value of v
indicates that the image is formed behind the mirror.

The
positive value of magnification indicates that the image formed is
virtual and erect.

Page No 186:

Question 13:

The magnification produced by a plane mirror is +1. What does this
mean?

Answer:

Magnification
produced by a mirror is given by the relation

The
magnification produced by a plane mirror is +1. It shows
that the image formed by the plane mirror is of the same size as that
of the object. The positive sign shows that the image formed is
virtual and erect.

Page No 186:

Question 14:

An
object 5.0 cm in length is placed at a distance
of 20 cm in front of a convex mirror of radius of curvature 30 cm.
Find the position of the image, its nature and size.

Answer:

Object
distance, u
= −20 cm

Object
height, h
= 5 cm

Radius
of curvature, R
= 30 cm

Radius
of curvature = 2 × Focal length

R
= 2f

f
= 15 cm

According
to the mirror formula,

The
positive value of v
indicates that the image is formed behind the mirror.

The
positive value of image height indicates that the image formed is
erect.

Therefore,
the image formed is virtual, erect, and
smaller in size.

Page No 186:

Question 15:

An
object of size 7.0 cm is placed at 27 cm in
front of a concave mirror of focal length 18 cm. At what distance
from the mirror should a screen be placed, so that a sharp focused
image can be obtained? Find the size and the nature of the image.

Answer:

Object
distance, u
= −27 cm

Object
height, h
= 7 cm

Focal
length, f =
−18 cm

According
to the mirror formula,

The screen
should be placed at a distance of 54 cm in front of the given mirror.

The
negative value of magnification indicates that the image formed is
real.

The
negative value of image height indicates that the image formed is
inverted.

Page No 186:

Question 16:

Find
the focal length of a lens of power −2.0
D. What type of lens is this?

Answer:

A concave
lens has a negative focal length. Hence, it is a concave lens.

Page No 186:

Question 17:

A
doctor has prescribed a corrective lens of
power +1.5 D. Find the focal length of the lens. Is the prescribed
lens diverging or converging?

Answer:

A convex
lens has a positive focal length. Hence, it is a convex lens or a
converging lens.